Field of the Invention
This invention relates to translators which combine a digital input and an analog input; and, more particularly, to translators which breaks the digital signal into components for which analog equivalents are determined and then combines them with the analog input.
Description of the Prior Art
Translators which provide an analog output from digital and analog inputs are known in the prior art. Prior art translators are known which utilize amplitude modulated sine wave signals from a resolver, which corresponds to an angular position of the resolver, and digital words in coded form, corresponding to the desired position of the resolver shaft, and provide an output signal equivalent to the difference. In general, translators perform the computation of the function sin (.theta. - .phi.) sin .omega.t where theta (.theta.) is the angle of the resolver and phi (.phi.) is the desired digital input. Sin .omega.t is a carrier whose envelopes define the trigonometric function under consideration. Throughout the following "sin .omega.t" will normally be ommitted since it provides no useful information and is only a carrier. That is, it is common in the prior art to explain the operations in trigonometric form without including the carrier. Prior art translators normally comput the function of sin (.theta. - .phi.) based on the following trigonometric identity: sin (.theta. - .phi.) = sin .theta. cos .phi. - cos .theta. sin .phi.. The functions, sin .theta. cos .phi., and, - cos .theta. sin .phi., are generated by operating two sets of analog switches on the resolver output and weighing the sin .theta. and cos .theta. terms by precision weighing networks corresponding to the weight of sin .phi. and cos .phi.. The quantities are then algebraically added to give the desired function. This method requires a large number of precision components which are expensive. Trigonometric functions are also sometimes solved by using a plurality of transformers having a plurality of taps to provide the desired trigonometric signals. This requires several specially built transformers and is relatively expensive.
Prior art U.S. Pat. No. 3,543,011 utilizes a trigonometric function to add or subtract two analog angles expressed in sine and cosine form. The apparatus disclosed in U.S. Pat. No. 3,543,011 uses a plurality of transformers having numerous taps to effect multiplication by a factor proportional to the tangent of one-half the angle to be added, in accordance with the mathematical properties of the sines and cosines of the sums or differences of the two angles.
Prior art U.S. Pat. Nos. 2,839,711; 2,849,668; and 2,967,017 teach digital to analog converters, for converting an input digital signal to an output analog signal in sine and cosine form. These prior art patents utilize a plurality of transformers having numerous taps which are interconnected in response to the input digital signal to provide the proper analog output. Rotary stepping switches are used for changing the connections of the plurality of transformers in response to the digital input. Prior art U.S. Pat. Nos. 2,849,668 and 2,967,017 recognize the use of the following trigonometric functions: sin (a + b)/cos b = tan b cos a + sin a; and, cos (a + b)/cos b = cos a - tan b sin a; when the corresponding vector angle b is small.
Prior art U.S. Pat. Nos. 2,839,711; 2,849,668; 2,967,017; and 3,543,011 have the disadvantage of requiring a plurality of specially built and expensive ratio transformers which have numerous taps. The apparatus disclosed in these prior art patents also utilize rotary stepping switches which are relatively slow acting and thus introduce unwanted time delays. Some prior art systems have utilized trigonometric equations involving the tangent for relatively small vector angles. These equations have never been applied to large angles, and in fact they are not directly solvable for some tangent angles. In particular the equations are indeterminate for tangent angles of 90.degree. and 270.degree..